Why my heels hurt when I get off from bed at night, hurts when I walk on it and its only on the right leg's heel?

Plantar fascitis. Inflammation of the plantar facia, or covering of the bottom of the foot is your most likely diagnosis. You may have developed a bone spur on the right or both heels, exacerbating the problem. You need to see a podiatrist, who will xray you feet to look for abnormal bone growth, recommend orthotics, topical or oral antinflammatants, a cortisone injection into the affected area, or a surgical fix.
Plantar fasciitis. . Sounds like plantar fasciitis. This commonly can be one sided. Get some thick silicone heel ups and do heel cord and plantar fascia stretches 3x a day at least. Consider a night splint to decrease the morning pain.